12bis. Mixture of logit with panel data and segmented ASCΒΆ

Variant of the panel mixed logit example where one ASC is segmented using the socio-economic variable MALE. This can be used to reproduce the panel renaming issue if shared Variable objects are renamed multiple times.

Michel Bierlaire, EPFL

from IPython.core.display_functions import display

See the data processing script: Panel data preparation for Swissmetro.

from swissmetro_panel import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    MALE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    database,
)

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta, Draws, MonteCarlo, PanelLikelihoodTrajectory, log
from biogeme.models import logit
from biogeme.results_processing import (
    EstimationResults,
    get_pandas_estimated_parameters,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info("Example b12_panel_segmented_male.py")
Example b12_panel_segmented_male.py

Parameters to be estimated.

b_cost = Beta("b_cost", 0, None, 0, 0)

Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation.

b_time = Beta("b_time", 0, None, 0, 0)

It is advised not to use 0 as starting value for the following parameter.

b_time_s = Beta("b_time_s", 1, 1.0e-5, None, 0)
b_time_rnd = b_time + b_time_s * Draws("b_time_rnd", "NORMAL_ANTI")

Random ASCs to address serial correlation.

asc_car = Beta("asc_car", 0, None, None, 0)
asc_car_s = Beta("asc_car_s", 1, 1.0e-5, None, 0)
asc_car_rnd = asc_car + asc_car_s * Draws("asc_car_rnd", "NORMAL_ANTI")

asc_train = Beta("asc_train", 0, None, None, 0)
asc_train_s = Beta("asc_train_s", 1, 1.0e-5, None, 0)
asc_train_rnd = asc_train + asc_train_s * Draws("asc_train_rnd", "NORMAL_ANTI")

asc_sm = Beta("asc_sm", 0, None, None, 0)
asc_sm_s = Beta("asc_sm_s", 1, 1.0e-5, None, 0)
asc_sm_rnd_base = asc_sm + asc_sm_s * Draws("asc_sm_rnd", "NORMAL_ANTI")

Segmentation of one ASC by the socioeconomic variable MALE. This is intentionally written in a way that reuses the same variable in a comparison expression, to reproduce the original issue.

asc_sm_male = Beta("asc_sm_male", 0, None, None, 0)
asc_sm_rnd = asc_sm_rnd_base + asc_sm_male * (MALE == 1)

asc_train_male = Beta("asc_train_male", 0, None, None, 0)
asc_sm_male = Beta("asc_sm_male", 0, None, None, 0)
asc_car_male = Beta("asc_car_male", 0, None, None, 0)

v_train = (
    asc_train_rnd
    + asc_train_male * (MALE == 1)
    + b_time_rnd * TRAIN_TT_SCALED
    + b_cost * TRAIN_COST_SCALED
)

v_swissmetro = (
    asc_sm_rnd_base
    + asc_sm_male * (MALE == 1)
    + b_time_rnd * SM_TT_SCALED
    + b_cost * SM_COST_SCALED
)

v_car = (
    asc_car_rnd
    + asc_car_male * (MALE == 1)
    + b_time_rnd * CAR_TT_SCALED
    + b_cost * CAR_CO_SCALED
)

Associate utility functions with the numbering of alternatives.

v = {1: v_train, 2: v_swissmetro, 3: v_car}

Associate the availability conditions with the alternatives.

av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}

Conditional on the random parameters, the likelihood of one observation is given by the logit model (called the kernel).

choice_probability_one_observation = logit(v, av, CHOICE)

Conditional on the random parameters, the likelihood of all observations for one individual (the trajectory) is the product of the likelihood of each observation.

conditional_trajectory_probability = PanelLikelihoodTrajectory(
    choice_probability_one_observation
)

We integrate over the random parameters using Monte-Carlo.

log_probability = log(MonteCarlo(conditional_trajectory_probability))
the_biogeme = BIOGEME(
    database,
    log_probability,
    number_of_draws=5_000,
    seed=1223,
    calculating_second_derivatives="never",
)
the_biogeme.model_name = "b12_panel_segmented_male"
Biogeme parameters read from biogeme.toml.

Estimate the parameters.

try:
    results = EstimationResults.from_yaml_file(
        filename=f"saved_results/{the_biogeme.model_name}.yaml"
    )
except FileNotFoundError:
    results = the_biogeme.estimate()
print(results.short_summary())
Results for model b12_panel_segmented_male
Nbr of parameters:              12
Sample size:                    752
Observations:                   6768
Excluded data:                  0
Final log likelihood:           -3543.843
Akaike Information Criterion:   7111.686
Bayesian Information Criterion: 7167.159
pandas_results = get_pandas_estimated_parameters(estimation_results=results)
display(pandas_results)
{'Estimated parameters':               Name     Value  ...  BHHH p-value  Active bound
0        asc_train  1.233454  ...  1.461649e-06         False
1      asc_train_s  2.521465  ...  0.000000e+00         False
2   asc_train_male -2.132275  ...  2.626788e-13         False
3           b_time -6.026511  ...  0.000000e+00         False
4         b_time_s  3.502407  ...  0.000000e+00         False
5           b_cost -3.523512  ...  0.000000e+00         False
6           asc_sm  0.029208  ...  8.770092e-01         False
7         asc_sm_s  0.000010  ...  9.999874e-01          True
8      asc_sm_male  0.178862  ...  3.960256e-01         False
9          asc_car -1.145479  ...  4.813668e-04         False
10       asc_car_s  3.925120  ...  0.000000e+00         False
11    asc_car_male  1.998629  ...  3.694476e-08         False

[12 rows x 6 columns]}

List of columns of the flat database generated by Biogeme.

for col in the_biogeme.model_elements.database.dataframe.columns:
    print(col)
GROUP
SURVEY
SP
ID
PURPOSE
FIRST
TICKET
WHO
LUGGAGE
AGE
MALE
INCOME
GA
ORIGIN
DEST
TRAIN_AV
CAR_AV
SM_AV
TRAIN_TT
TRAIN_CO
TRAIN_HE
SM_TT
SM_CO
SM_HE
SM_SEATS
CAR_TT
CAR_CO
CHOICE
SM_COST
TRAIN_COST
CAR_AV_SP
TRAIN_AV_SP
TRAIN_TT_SCALED
TRAIN_COST_SCALED
SM_TT_SCALED
SM_COST_SCALED
CAR_TT_SCALED
CAR_CO_SCALED

List of variables that have been renamed in the model specification.

for var in the_biogeme.model_elements.expressions_registry.variables:
    print(var)
GROUP
SURVEY
SP
ID
PURPOSE
FIRST
TICKET
WHO
LUGGAGE
AGE
MALE
INCOME
GA
ORIGIN
DEST
TRAIN_AV
CAR_AV
SM_AV
TRAIN_TT
TRAIN_CO
TRAIN_HE
SM_TT
SM_CO
SM_HE
SM_SEATS
CAR_TT
CAR_CO
CHOICE
SM_COST
TRAIN_COST
CAR_AV_SP
TRAIN_AV_SP
TRAIN_TT_SCALED
TRAIN_COST_SCALED
SM_TT_SCALED
SM_COST_SCALED
CAR_TT_SCALED
CAR_CO_SCALED

Total running time of the script: (0 minutes 0.114 seconds)

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